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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 01 Apr 2015 17:54:46 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/01/t1427907320s6429thjf13i2nb.htm/, Retrieved Thu, 09 May 2024 07:37:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278527, Retrieved Thu, 09 May 2024 07:37:22 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

148

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [] [2015-04-01 16:54:46] [478e7c199ef13b68c565592d49c085e5] [Current]

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Dataseries X:

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4,8
4,81
5,16
5,26
5,29
5,29
5,29
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,35
5,44
5,47
5,47
5,48
5,48
5,48
5,48
5,48
5,48
5,48
5,5
5,55
5,57
5,58
5,58
5,58
5,59
5,59
5,59
5,55
5,61
5,61
5,61
5,63
5,69
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,71
5,74
5,77
5,79
5,79
5,8
5,8
5,8
5,8
5,8
5,81
5,81
5,83
5,94
5,98
5,99
6
6,02
6,02
6,02
6,02
6,02
6,02
6,02
6,04
6,06
6,06
6,07
6,14
6,19
6,2
6,22
6,22

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278527&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278527&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278527&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.00580523703724111
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00580523703724111 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278527&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.00580523703724111[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278527&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278527&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.00580523703724111
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	5.16	4.82	0.340000000000001
4	5.26	5.17197378059266	0.0880262194073378
5	5.29	5.27248479366181	0.0175152063381869
6	5.29	5.30258647358636	-0.0125864735863628
7	5.29	5.30251340612373	-0.0125134061237313
8	5.3	5.30244076283504	-0.00244076283503958
9	5.3	5.31242659362823	-0.0124265936282306
10	5.3	5.31235445430665	-0.0123544543066529
11	5.3	5.31228273377094	-0.0122827337709372
12	5.3	5.31221142958993	-0.0122114295899314
13	5.3	5.3121405393466	-0.0121405393465981
14	5.3	5.31207006063793	-0.0120700606379316
15	5.3	5.31199999107487	-0.011999991074874
16	5.35	5.31193032828224	0.0380696717177598
17	5.44	5.36215133175049	0.0778486682495094
18	5.47	5.45260326172271	0.0173967382772862
19	5.47	5.48270425391209	-0.0127042539120881
20	5.48	5.48263050270675	-0.00263050270674636
21	5.48	5.49261523201501	-0.0126152320150075
22	5.48	5.49254199760288	-0.01254199760288
23	5.48	5.49246918833388	-0.012469188333875
24	5.48	5.49239680173994	-0.0123968017399347
25	5.48	5.49232483536733	-0.0123248353673313
26	5.48	5.49225328677658	-0.0122532867765788
27	5.5	5.49218215354236	0.00781784645764461
28	5.55	5.51222753799416	0.0377724620058375
29	5.57	5.56244681608959	0.00755318391041371
30	5.58	5.58249066411257	-0.00249066411257282
31	5.58	5.59247620521702	-0.0124762052170189
32	5.58	5.59240377788841	-0.0124037778884087
33	5.59	5.59233177101761	-0.00233177101760962
34	5.59	5.60231823453414	-0.0123182345341357
35	5.59	5.60224672426278	-0.0122467242627851
36	5.55	5.60217562912551	-0.0521756291255091
37	5.61	5.56187273723087	0.0481272627691318
38	5.61	5.6221521273992	-0.0121521273991974
39	5.61	5.62208158141914	-0.012081581419138
40	5.63	5.62201144497522	0.00798855502478446
41	5.69	5.64205782043072	0.0479421795692812
42	5.7	5.7023361361472	-0.00233613614720074
43	5.7	5.71232257432311	-0.0123225743231146
44	5.7	5.71225103885826	-0.0122510388582606
45	5.7	5.71217991867374	-0.0121799186737359
46	5.7	5.71210921135874	-0.01210921135874
47	5.7	5.71203891451647	-0.0120389145164683
48	5.7	5.71196902576403	-0.0119690257640297
49	5.7	5.71189954273236	-0.0118995427323645
50	5.7	5.71183046306617	-0.0118304630661683
51	5.7	5.71176178442381	-0.0117617844238085
52	5.71	5.71169350447725	-0.00169350447724792
53	5.74	5.72168367328233	0.0183163267176667
54	5.77	5.75179000390058	0.0182099960994178
55	5.79	5.78189571724439	0.00810428275561481
56	5.79	5.8019427645268	-0.0119427645267987
57	5.8	5.80187343394784	-0.00187343394784101
58	5.8	5.8118625582197	-0.0118625582196996
59	5.8	5.81179369325737	-0.0117936932573661
60	5.8	5.81172522807246	-0.0117252280724633
61	5.8	5.81165716034419	-0.0116571603441864
62	5.81	5.81158948776521	-0.00158948776520784
63	5.81	5.82158026041196	-0.0115802604119626
64	5.83	5.82151303425532	0.008486965744682
65	5.94	5.84156230310319	0.0984376968968075
66	5.98	5.95213375726708	0.0278662427329213
67	5.99	5.99229552741148	-0.00229552741148087
68	6	6.00228220133073	-0.00228220133073176
69	6.02	6.01226895261104	0.00773104738895913
70	6.02	6.03231383317368	-0.0123138331736792
71	6.02	6.03224234845327	-0.0122423484532694
72	6.02	6.0321712787186	-0.012171278718605
73	6.02	6.0321006215606	-0.0121006215605979
74	6.02	6.03203037458414	-0.0120303745841408
75	6.02	6.03196053540803	-0.0119605354080328
76	6.04	6.0318911016649	0.00810889833510409
77	6.06	6.05193817574184	0.00806182425815649
78	6.06	6.07198497654261	-0.0119849765426139
79	6.07	6.0719154009129	-0.00191540091289788
80	6.14	6.08190428155658	0.0580957184434219
81	6.19	6.15224154097299	0.0377584590270104
82	6.2	6.2024607377778	-0.00246073777780342
83	6.22	6.21244645261172	0.00755354738828284
84	6.22	6.23249030274478	-0.0124903027447774

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5.16 & 4.82 & 0.340000000000001 \tabularnewline
4 & 5.26 & 5.17197378059266 & 0.0880262194073378 \tabularnewline
5 & 5.29 & 5.27248479366181 & 0.0175152063381869 \tabularnewline
6 & 5.29 & 5.30258647358636 & -0.0125864735863628 \tabularnewline
7 & 5.29 & 5.30251340612373 & -0.0125134061237313 \tabularnewline
8 & 5.3 & 5.30244076283504 & -0.00244076283503958 \tabularnewline
9 & 5.3 & 5.31242659362823 & -0.0124265936282306 \tabularnewline
10 & 5.3 & 5.31235445430665 & -0.0123544543066529 \tabularnewline
11 & 5.3 & 5.31228273377094 & -0.0122827337709372 \tabularnewline
12 & 5.3 & 5.31221142958993 & -0.0122114295899314 \tabularnewline
13 & 5.3 & 5.3121405393466 & -0.0121405393465981 \tabularnewline
14 & 5.3 & 5.31207006063793 & -0.0120700606379316 \tabularnewline
15 & 5.3 & 5.31199999107487 & -0.011999991074874 \tabularnewline
16 & 5.35 & 5.31193032828224 & 0.0380696717177598 \tabularnewline
17 & 5.44 & 5.36215133175049 & 0.0778486682495094 \tabularnewline
18 & 5.47 & 5.45260326172271 & 0.0173967382772862 \tabularnewline
19 & 5.47 & 5.48270425391209 & -0.0127042539120881 \tabularnewline
20 & 5.48 & 5.48263050270675 & -0.00263050270674636 \tabularnewline
21 & 5.48 & 5.49261523201501 & -0.0126152320150075 \tabularnewline
22 & 5.48 & 5.49254199760288 & -0.01254199760288 \tabularnewline
23 & 5.48 & 5.49246918833388 & -0.012469188333875 \tabularnewline
24 & 5.48 & 5.49239680173994 & -0.0123968017399347 \tabularnewline
25 & 5.48 & 5.49232483536733 & -0.0123248353673313 \tabularnewline
26 & 5.48 & 5.49225328677658 & -0.0122532867765788 \tabularnewline
27 & 5.5 & 5.49218215354236 & 0.00781784645764461 \tabularnewline
28 & 5.55 & 5.51222753799416 & 0.0377724620058375 \tabularnewline
29 & 5.57 & 5.56244681608959 & 0.00755318391041371 \tabularnewline
30 & 5.58 & 5.58249066411257 & -0.00249066411257282 \tabularnewline
31 & 5.58 & 5.59247620521702 & -0.0124762052170189 \tabularnewline
32 & 5.58 & 5.59240377788841 & -0.0124037778884087 \tabularnewline
33 & 5.59 & 5.59233177101761 & -0.00233177101760962 \tabularnewline
34 & 5.59 & 5.60231823453414 & -0.0123182345341357 \tabularnewline
35 & 5.59 & 5.60224672426278 & -0.0122467242627851 \tabularnewline
36 & 5.55 & 5.60217562912551 & -0.0521756291255091 \tabularnewline
37 & 5.61 & 5.56187273723087 & 0.0481272627691318 \tabularnewline
38 & 5.61 & 5.6221521273992 & -0.0121521273991974 \tabularnewline
39 & 5.61 & 5.62208158141914 & -0.012081581419138 \tabularnewline
40 & 5.63 & 5.62201144497522 & 0.00798855502478446 \tabularnewline
41 & 5.69 & 5.64205782043072 & 0.0479421795692812 \tabularnewline
42 & 5.7 & 5.7023361361472 & -0.00233613614720074 \tabularnewline
43 & 5.7 & 5.71232257432311 & -0.0123225743231146 \tabularnewline
44 & 5.7 & 5.71225103885826 & -0.0122510388582606 \tabularnewline
45 & 5.7 & 5.71217991867374 & -0.0121799186737359 \tabularnewline
46 & 5.7 & 5.71210921135874 & -0.01210921135874 \tabularnewline
47 & 5.7 & 5.71203891451647 & -0.0120389145164683 \tabularnewline
48 & 5.7 & 5.71196902576403 & -0.0119690257640297 \tabularnewline
49 & 5.7 & 5.71189954273236 & -0.0118995427323645 \tabularnewline
50 & 5.7 & 5.71183046306617 & -0.0118304630661683 \tabularnewline
51 & 5.7 & 5.71176178442381 & -0.0117617844238085 \tabularnewline
52 & 5.71 & 5.71169350447725 & -0.00169350447724792 \tabularnewline
53 & 5.74 & 5.72168367328233 & 0.0183163267176667 \tabularnewline
54 & 5.77 & 5.75179000390058 & 0.0182099960994178 \tabularnewline
55 & 5.79 & 5.78189571724439 & 0.00810428275561481 \tabularnewline
56 & 5.79 & 5.8019427645268 & -0.0119427645267987 \tabularnewline
57 & 5.8 & 5.80187343394784 & -0.00187343394784101 \tabularnewline
58 & 5.8 & 5.8118625582197 & -0.0118625582196996 \tabularnewline
59 & 5.8 & 5.81179369325737 & -0.0117936932573661 \tabularnewline
60 & 5.8 & 5.81172522807246 & -0.0117252280724633 \tabularnewline
61 & 5.8 & 5.81165716034419 & -0.0116571603441864 \tabularnewline
62 & 5.81 & 5.81158948776521 & -0.00158948776520784 \tabularnewline
63 & 5.81 & 5.82158026041196 & -0.0115802604119626 \tabularnewline
64 & 5.83 & 5.82151303425532 & 0.008486965744682 \tabularnewline
65 & 5.94 & 5.84156230310319 & 0.0984376968968075 \tabularnewline
66 & 5.98 & 5.95213375726708 & 0.0278662427329213 \tabularnewline
67 & 5.99 & 5.99229552741148 & -0.00229552741148087 \tabularnewline
68 & 6 & 6.00228220133073 & -0.00228220133073176 \tabularnewline
69 & 6.02 & 6.01226895261104 & 0.00773104738895913 \tabularnewline
70 & 6.02 & 6.03231383317368 & -0.0123138331736792 \tabularnewline
71 & 6.02 & 6.03224234845327 & -0.0122423484532694 \tabularnewline
72 & 6.02 & 6.0321712787186 & -0.012171278718605 \tabularnewline
73 & 6.02 & 6.0321006215606 & -0.0121006215605979 \tabularnewline
74 & 6.02 & 6.03203037458414 & -0.0120303745841408 \tabularnewline
75 & 6.02 & 6.03196053540803 & -0.0119605354080328 \tabularnewline
76 & 6.04 & 6.0318911016649 & 0.00810889833510409 \tabularnewline
77 & 6.06 & 6.05193817574184 & 0.00806182425815649 \tabularnewline
78 & 6.06 & 6.07198497654261 & -0.0119849765426139 \tabularnewline
79 & 6.07 & 6.0719154009129 & -0.00191540091289788 \tabularnewline
80 & 6.14 & 6.08190428155658 & 0.0580957184434219 \tabularnewline
81 & 6.19 & 6.15224154097299 & 0.0377584590270104 \tabularnewline
82 & 6.2 & 6.2024607377778 & -0.00246073777780342 \tabularnewline
83 & 6.22 & 6.21244645261172 & 0.00755354738828284 \tabularnewline
84 & 6.22 & 6.23249030274478 & -0.0124903027447774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278527&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]5.16[/C][C]4.82[/C][C]0.340000000000001[/C][/ROW]
[ROW][C]4[/C][C]5.26[/C][C]5.17197378059266[/C][C]0.0880262194073378[/C][/ROW]
[ROW][C]5[/C][C]5.29[/C][C]5.27248479366181[/C][C]0.0175152063381869[/C][/ROW]
[ROW][C]6[/C][C]5.29[/C][C]5.30258647358636[/C][C]-0.0125864735863628[/C][/ROW]
[ROW][C]7[/C][C]5.29[/C][C]5.30251340612373[/C][C]-0.0125134061237313[/C][/ROW]
[ROW][C]8[/C][C]5.3[/C][C]5.30244076283504[/C][C]-0.00244076283503958[/C][/ROW]
[ROW][C]9[/C][C]5.3[/C][C]5.31242659362823[/C][C]-0.0124265936282306[/C][/ROW]
[ROW][C]10[/C][C]5.3[/C][C]5.31235445430665[/C][C]-0.0123544543066529[/C][/ROW]
[ROW][C]11[/C][C]5.3[/C][C]5.31228273377094[/C][C]-0.0122827337709372[/C][/ROW]
[ROW][C]12[/C][C]5.3[/C][C]5.31221142958993[/C][C]-0.0122114295899314[/C][/ROW]
[ROW][C]13[/C][C]5.3[/C][C]5.3121405393466[/C][C]-0.0121405393465981[/C][/ROW]
[ROW][C]14[/C][C]5.3[/C][C]5.31207006063793[/C][C]-0.0120700606379316[/C][/ROW]
[ROW][C]15[/C][C]5.3[/C][C]5.31199999107487[/C][C]-0.011999991074874[/C][/ROW]
[ROW][C]16[/C][C]5.35[/C][C]5.31193032828224[/C][C]0.0380696717177598[/C][/ROW]
[ROW][C]17[/C][C]5.44[/C][C]5.36215133175049[/C][C]0.0778486682495094[/C][/ROW]
[ROW][C]18[/C][C]5.47[/C][C]5.45260326172271[/C][C]0.0173967382772862[/C][/ROW]
[ROW][C]19[/C][C]5.47[/C][C]5.48270425391209[/C][C]-0.0127042539120881[/C][/ROW]
[ROW][C]20[/C][C]5.48[/C][C]5.48263050270675[/C][C]-0.00263050270674636[/C][/ROW]
[ROW][C]21[/C][C]5.48[/C][C]5.49261523201501[/C][C]-0.0126152320150075[/C][/ROW]
[ROW][C]22[/C][C]5.48[/C][C]5.49254199760288[/C][C]-0.01254199760288[/C][/ROW]
[ROW][C]23[/C][C]5.48[/C][C]5.49246918833388[/C][C]-0.012469188333875[/C][/ROW]
[ROW][C]24[/C][C]5.48[/C][C]5.49239680173994[/C][C]-0.0123968017399347[/C][/ROW]
[ROW][C]25[/C][C]5.48[/C][C]5.49232483536733[/C][C]-0.0123248353673313[/C][/ROW]
[ROW][C]26[/C][C]5.48[/C][C]5.49225328677658[/C][C]-0.0122532867765788[/C][/ROW]
[ROW][C]27[/C][C]5.5[/C][C]5.49218215354236[/C][C]0.00781784645764461[/C][/ROW]
[ROW][C]28[/C][C]5.55[/C][C]5.51222753799416[/C][C]0.0377724620058375[/C][/ROW]
[ROW][C]29[/C][C]5.57[/C][C]5.56244681608959[/C][C]0.00755318391041371[/C][/ROW]
[ROW][C]30[/C][C]5.58[/C][C]5.58249066411257[/C][C]-0.00249066411257282[/C][/ROW]
[ROW][C]31[/C][C]5.58[/C][C]5.59247620521702[/C][C]-0.0124762052170189[/C][/ROW]
[ROW][C]32[/C][C]5.58[/C][C]5.59240377788841[/C][C]-0.0124037778884087[/C][/ROW]
[ROW][C]33[/C][C]5.59[/C][C]5.59233177101761[/C][C]-0.00233177101760962[/C][/ROW]
[ROW][C]34[/C][C]5.59[/C][C]5.60231823453414[/C][C]-0.0123182345341357[/C][/ROW]
[ROW][C]35[/C][C]5.59[/C][C]5.60224672426278[/C][C]-0.0122467242627851[/C][/ROW]
[ROW][C]36[/C][C]5.55[/C][C]5.60217562912551[/C][C]-0.0521756291255091[/C][/ROW]
[ROW][C]37[/C][C]5.61[/C][C]5.56187273723087[/C][C]0.0481272627691318[/C][/ROW]
[ROW][C]38[/C][C]5.61[/C][C]5.6221521273992[/C][C]-0.0121521273991974[/C][/ROW]
[ROW][C]39[/C][C]5.61[/C][C]5.62208158141914[/C][C]-0.012081581419138[/C][/ROW]
[ROW][C]40[/C][C]5.63[/C][C]5.62201144497522[/C][C]0.00798855502478446[/C][/ROW]
[ROW][C]41[/C][C]5.69[/C][C]5.64205782043072[/C][C]0.0479421795692812[/C][/ROW]
[ROW][C]42[/C][C]5.7[/C][C]5.7023361361472[/C][C]-0.00233613614720074[/C][/ROW]
[ROW][C]43[/C][C]5.7[/C][C]5.71232257432311[/C][C]-0.0123225743231146[/C][/ROW]
[ROW][C]44[/C][C]5.7[/C][C]5.71225103885826[/C][C]-0.0122510388582606[/C][/ROW]
[ROW][C]45[/C][C]5.7[/C][C]5.71217991867374[/C][C]-0.0121799186737359[/C][/ROW]
[ROW][C]46[/C][C]5.7[/C][C]5.71210921135874[/C][C]-0.01210921135874[/C][/ROW]
[ROW][C]47[/C][C]5.7[/C][C]5.71203891451647[/C][C]-0.0120389145164683[/C][/ROW]
[ROW][C]48[/C][C]5.7[/C][C]5.71196902576403[/C][C]-0.0119690257640297[/C][/ROW]
[ROW][C]49[/C][C]5.7[/C][C]5.71189954273236[/C][C]-0.0118995427323645[/C][/ROW]
[ROW][C]50[/C][C]5.7[/C][C]5.71183046306617[/C][C]-0.0118304630661683[/C][/ROW]
[ROW][C]51[/C][C]5.7[/C][C]5.71176178442381[/C][C]-0.0117617844238085[/C][/ROW]
[ROW][C]52[/C][C]5.71[/C][C]5.71169350447725[/C][C]-0.00169350447724792[/C][/ROW]
[ROW][C]53[/C][C]5.74[/C][C]5.72168367328233[/C][C]0.0183163267176667[/C][/ROW]
[ROW][C]54[/C][C]5.77[/C][C]5.75179000390058[/C][C]0.0182099960994178[/C][/ROW]
[ROW][C]55[/C][C]5.79[/C][C]5.78189571724439[/C][C]0.00810428275561481[/C][/ROW]
[ROW][C]56[/C][C]5.79[/C][C]5.8019427645268[/C][C]-0.0119427645267987[/C][/ROW]
[ROW][C]57[/C][C]5.8[/C][C]5.80187343394784[/C][C]-0.00187343394784101[/C][/ROW]
[ROW][C]58[/C][C]5.8[/C][C]5.8118625582197[/C][C]-0.0118625582196996[/C][/ROW]
[ROW][C]59[/C][C]5.8[/C][C]5.81179369325737[/C][C]-0.0117936932573661[/C][/ROW]
[ROW][C]60[/C][C]5.8[/C][C]5.81172522807246[/C][C]-0.0117252280724633[/C][/ROW]
[ROW][C]61[/C][C]5.8[/C][C]5.81165716034419[/C][C]-0.0116571603441864[/C][/ROW]
[ROW][C]62[/C][C]5.81[/C][C]5.81158948776521[/C][C]-0.00158948776520784[/C][/ROW]
[ROW][C]63[/C][C]5.81[/C][C]5.82158026041196[/C][C]-0.0115802604119626[/C][/ROW]
[ROW][C]64[/C][C]5.83[/C][C]5.82151303425532[/C][C]0.008486965744682[/C][/ROW]
[ROW][C]65[/C][C]5.94[/C][C]5.84156230310319[/C][C]0.0984376968968075[/C][/ROW]
[ROW][C]66[/C][C]5.98[/C][C]5.95213375726708[/C][C]0.0278662427329213[/C][/ROW]
[ROW][C]67[/C][C]5.99[/C][C]5.99229552741148[/C][C]-0.00229552741148087[/C][/ROW]
[ROW][C]68[/C][C]6[/C][C]6.00228220133073[/C][C]-0.00228220133073176[/C][/ROW]
[ROW][C]69[/C][C]6.02[/C][C]6.01226895261104[/C][C]0.00773104738895913[/C][/ROW]
[ROW][C]70[/C][C]6.02[/C][C]6.03231383317368[/C][C]-0.0123138331736792[/C][/ROW]
[ROW][C]71[/C][C]6.02[/C][C]6.03224234845327[/C][C]-0.0122423484532694[/C][/ROW]
[ROW][C]72[/C][C]6.02[/C][C]6.0321712787186[/C][C]-0.012171278718605[/C][/ROW]
[ROW][C]73[/C][C]6.02[/C][C]6.0321006215606[/C][C]-0.0121006215605979[/C][/ROW]
[ROW][C]74[/C][C]6.02[/C][C]6.03203037458414[/C][C]-0.0120303745841408[/C][/ROW]
[ROW][C]75[/C][C]6.02[/C][C]6.03196053540803[/C][C]-0.0119605354080328[/C][/ROW]
[ROW][C]76[/C][C]6.04[/C][C]6.0318911016649[/C][C]0.00810889833510409[/C][/ROW]
[ROW][C]77[/C][C]6.06[/C][C]6.05193817574184[/C][C]0.00806182425815649[/C][/ROW]
[ROW][C]78[/C][C]6.06[/C][C]6.07198497654261[/C][C]-0.0119849765426139[/C][/ROW]
[ROW][C]79[/C][C]6.07[/C][C]6.0719154009129[/C][C]-0.00191540091289788[/C][/ROW]
[ROW][C]80[/C][C]6.14[/C][C]6.08190428155658[/C][C]0.0580957184434219[/C][/ROW]
[ROW][C]81[/C][C]6.19[/C][C]6.15224154097299[/C][C]0.0377584590270104[/C][/ROW]
[ROW][C]82[/C][C]6.2[/C][C]6.2024607377778[/C][C]-0.00246073777780342[/C][/ROW]
[ROW][C]83[/C][C]6.22[/C][C]6.21244645261172[/C][C]0.00755354738828284[/C][/ROW]
[ROW][C]84[/C][C]6.22[/C][C]6.23249030274478[/C][C]-0.0124903027447774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278527&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278527&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	5.16	4.82	0.340000000000001
4	5.26	5.17197378059266	0.0880262194073378
5	5.29	5.27248479366181	0.0175152063381869
6	5.29	5.30258647358636	-0.0125864735863628
7	5.29	5.30251340612373	-0.0125134061237313
8	5.3	5.30244076283504	-0.00244076283503958
9	5.3	5.31242659362823	-0.0124265936282306
10	5.3	5.31235445430665	-0.0123544543066529
11	5.3	5.31228273377094	-0.0122827337709372
12	5.3	5.31221142958993	-0.0122114295899314
13	5.3	5.3121405393466	-0.0121405393465981
14	5.3	5.31207006063793	-0.0120700606379316
15	5.3	5.31199999107487	-0.011999991074874
16	5.35	5.31193032828224	0.0380696717177598
17	5.44	5.36215133175049	0.0778486682495094
18	5.47	5.45260326172271	0.0173967382772862
19	5.47	5.48270425391209	-0.0127042539120881
20	5.48	5.48263050270675	-0.00263050270674636
21	5.48	5.49261523201501	-0.0126152320150075
22	5.48	5.49254199760288	-0.01254199760288
23	5.48	5.49246918833388	-0.012469188333875
24	5.48	5.49239680173994	-0.0123968017399347
25	5.48	5.49232483536733	-0.0123248353673313
26	5.48	5.49225328677658	-0.0122532867765788
27	5.5	5.49218215354236	0.00781784645764461
28	5.55	5.51222753799416	0.0377724620058375
29	5.57	5.56244681608959	0.00755318391041371
30	5.58	5.58249066411257	-0.00249066411257282
31	5.58	5.59247620521702	-0.0124762052170189
32	5.58	5.59240377788841	-0.0124037778884087
33	5.59	5.59233177101761	-0.00233177101760962
34	5.59	5.60231823453414	-0.0123182345341357
35	5.59	5.60224672426278	-0.0122467242627851
36	5.55	5.60217562912551	-0.0521756291255091
37	5.61	5.56187273723087	0.0481272627691318
38	5.61	5.6221521273992	-0.0121521273991974
39	5.61	5.62208158141914	-0.012081581419138
40	5.63	5.62201144497522	0.00798855502478446
41	5.69	5.64205782043072	0.0479421795692812
42	5.7	5.7023361361472	-0.00233613614720074
43	5.7	5.71232257432311	-0.0123225743231146
44	5.7	5.71225103885826	-0.0122510388582606
45	5.7	5.71217991867374	-0.0121799186737359
46	5.7	5.71210921135874	-0.01210921135874
47	5.7	5.71203891451647	-0.0120389145164683
48	5.7	5.71196902576403	-0.0119690257640297
49	5.7	5.71189954273236	-0.0118995427323645
50	5.7	5.71183046306617	-0.0118304630661683
51	5.7	5.71176178442381	-0.0117617844238085
52	5.71	5.71169350447725	-0.00169350447724792
53	5.74	5.72168367328233	0.0183163267176667
54	5.77	5.75179000390058	0.0182099960994178
55	5.79	5.78189571724439	0.00810428275561481
56	5.79	5.8019427645268	-0.0119427645267987
57	5.8	5.80187343394784	-0.00187343394784101
58	5.8	5.8118625582197	-0.0118625582196996
59	5.8	5.81179369325737	-0.0117936932573661
60	5.8	5.81172522807246	-0.0117252280724633
61	5.8	5.81165716034419	-0.0116571603441864
62	5.81	5.81158948776521	-0.00158948776520784
63	5.81	5.82158026041196	-0.0115802604119626
64	5.83	5.82151303425532	0.008486965744682
65	5.94	5.84156230310319	0.0984376968968075
66	5.98	5.95213375726708	0.0278662427329213
67	5.99	5.99229552741148	-0.00229552741148087
68	6	6.00228220133073	-0.00228220133073176
69	6.02	6.01226895261104	0.00773104738895913
70	6.02	6.03231383317368	-0.0123138331736792
71	6.02	6.03224234845327	-0.0122423484532694
72	6.02	6.0321712787186	-0.012171278718605
73	6.02	6.0321006215606	-0.0121006215605979
74	6.02	6.03203037458414	-0.0120303745841408
75	6.02	6.03196053540803	-0.0119605354080328
76	6.04	6.0318911016649	0.00810889833510409
77	6.06	6.05193817574184	0.00806182425815649
78	6.06	6.07198497654261	-0.0119849765426139
79	6.07	6.0719154009129	-0.00191540091289788
80	6.14	6.08190428155658	0.0580957184434219
81	6.19	6.15224154097299	0.0377584590270104
82	6.2	6.2024607377778	-0.00246073777780342
83	6.22	6.21244645261172	0.00755354738828284
84	6.22	6.23249030274478	-0.0124903027447774

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	6.23241779357668	6.1449420051736	6.31989358197976
86	6.24483558715335	6.12076653985589	6.36890463445082
87	6.25725338073003	6.10485961255269	6.40964714890737
88	6.26967117430671	6.09319249128717	6.44614985732625
89	6.28208896788339	6.08420961272482	6.47996832304195
90	6.29450676146006	6.07711559961149	6.51189792330864
91	6.30692455503674	6.07143936341394	6.54240974665954
92	6.31934234861342	6.0668748662977	6.57180983092914
93	6.3317601421901	6.06321015528429	6.6003101290959
94	6.34417793576677	6.06029135850034	6.62806451303321
95	6.35659572934345	6.05800265300164	6.65518880568526
96	6.36901352292013	6.05625431732202	6.68177272851823

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 6.23241779357668 & 6.1449420051736 & 6.31989358197976 \tabularnewline
86 & 6.24483558715335 & 6.12076653985589 & 6.36890463445082 \tabularnewline
87 & 6.25725338073003 & 6.10485961255269 & 6.40964714890737 \tabularnewline
88 & 6.26967117430671 & 6.09319249128717 & 6.44614985732625 \tabularnewline
89 & 6.28208896788339 & 6.08420961272482 & 6.47996832304195 \tabularnewline
90 & 6.29450676146006 & 6.07711559961149 & 6.51189792330864 \tabularnewline
91 & 6.30692455503674 & 6.07143936341394 & 6.54240974665954 \tabularnewline
92 & 6.31934234861342 & 6.0668748662977 & 6.57180983092914 \tabularnewline
93 & 6.3317601421901 & 6.06321015528429 & 6.6003101290959 \tabularnewline
94 & 6.34417793576677 & 6.06029135850034 & 6.62806451303321 \tabularnewline
95 & 6.35659572934345 & 6.05800265300164 & 6.65518880568526 \tabularnewline
96 & 6.36901352292013 & 6.05625431732202 & 6.68177272851823 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278527&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]6.23241779357668[/C][C]6.1449420051736[/C][C]6.31989358197976[/C][/ROW]
[ROW][C]86[/C][C]6.24483558715335[/C][C]6.12076653985589[/C][C]6.36890463445082[/C][/ROW]
[ROW][C]87[/C][C]6.25725338073003[/C][C]6.10485961255269[/C][C]6.40964714890737[/C][/ROW]
[ROW][C]88[/C][C]6.26967117430671[/C][C]6.09319249128717[/C][C]6.44614985732625[/C][/ROW]
[ROW][C]89[/C][C]6.28208896788339[/C][C]6.08420961272482[/C][C]6.47996832304195[/C][/ROW]
[ROW][C]90[/C][C]6.29450676146006[/C][C]6.07711559961149[/C][C]6.51189792330864[/C][/ROW]
[ROW][C]91[/C][C]6.30692455503674[/C][C]6.07143936341394[/C][C]6.54240974665954[/C][/ROW]
[ROW][C]92[/C][C]6.31934234861342[/C][C]6.0668748662977[/C][C]6.57180983092914[/C][/ROW]
[ROW][C]93[/C][C]6.3317601421901[/C][C]6.06321015528429[/C][C]6.6003101290959[/C][/ROW]
[ROW][C]94[/C][C]6.34417793576677[/C][C]6.06029135850034[/C][C]6.62806451303321[/C][/ROW]
[ROW][C]95[/C][C]6.35659572934345[/C][C]6.05800265300164[/C][C]6.65518880568526[/C][/ROW]
[ROW][C]96[/C][C]6.36901352292013[/C][C]6.05625431732202[/C][C]6.68177272851823[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278527&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278527&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	6.23241779357668	6.1449420051736	6.31989358197976
86	6.24483558715335	6.12076653985589	6.36890463445082
87	6.25725338073003	6.10485961255269	6.40964714890737
88	6.26967117430671	6.09319249128717	6.44614985732625
89	6.28208896788339	6.08420961272482	6.47996832304195
90	6.29450676146006	6.07711559961149	6.51189792330864
91	6.30692455503674	6.07143936341394	6.54240974665954
92	6.31934234861342	6.0668748662977	6.57180983092914
93	6.3317601421901	6.06321015528429	6.6003101290959
94	6.34417793576677	6.06029135850034	6.62806451303321
95	6.35659572934345	6.05800265300164	6.65518880568526
96	6.36901352292013	6.05625431732202	6.68177272851823

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code